It would depend on how much time you want to spend and I agree, both are great places.
In Ecuador, you can access many biomes from Quito: In the east side of the Andes: Papallacta, Guango, and Cabañas de San Isidro, Wild Sumaco all the way to the lowlands where you can explore a number of lowland lodges. This gives you a good amount of birds to find. Also on the West Side, you could visit Mindo for some Choco specialties. Again, depending on your time availability, you could continue or start in Guayaquil and go south for Tumbesian region birds and then continue to Loja, Zamora where you could have great birding at the Podocarpus national park and tapichalaca reserve.
In the Pantanal, from Cuiaba, you could access to three different biomes. The Pantanal, the largest marsh in the world, Cerrado and the southernmost extension of the Amazon at Cristalino Lodge which is spectacular.
In terms of time, I don't know how much time you are thinking to spend on the trip but I have led tours to both places and depending on species people wanted to see this trips ranged from a week to 2 weeks. In Ecuador doing a trip from Quito all the way to the lowlands in the Amazon for instance. In the Pantanal, visiting the three biomes at once too.
Anyway, many things to have on mind but I hope this helps somehow.
Cheers
Pepe